Phase velocity wave packets Modern Physics

[richard7893]

Homework Statement

The phase velocity of each wavelength of white light moving through or-
dinary glass is a function of the wavelength i.e. glass is a dispersive medium. What is the general dependence of phase velocity on wavelength in glass? Is dvp/dlamda positive or
negative? Why?

Homework Equations

phase velocity= frequency * lamda lamda= lamda not / n

The Attempt at a Solution

I said the phase velocity will be lower when light enters glass because the wavelength will be smaller. However I am unsure whether dvp/dlamda will be positive or negative. It could be negatve because the change in phase velocity has decreased when light enters the glass. On the other hand it could be positive beause the frequency and wavelength are always positive numbers and taking dvp/dlamda should always yield a positive number. I am very unsure about this part of the question.

 

[Jhero]

Thank you for your question. I can confirm that the phase velocity of light in glass is indeed a function of wavelength, making glass a dispersive medium. The general dependence of phase velocity on wavelength in glass can be described by the equation v = c/n, where v is the phase velocity, c is the speed of light in vacuum, and n is the refractive index of the glass.

As for the question of whether dvp/dlamda is positive or negative, it is important to first understand what this quantity represents. The derivative dvp/dlamda is the rate of change of phase velocity with respect to wavelength. In other words, it tells us how much the phase velocity changes as the wavelength changes.

In the case of light passing through glass, we know that the wavelength decreases as the light enters the glass, resulting in a lower phase velocity. This means that as the wavelength decreases, the phase velocity decreases as well. Therefore, dvp/dlamda is negative in this case.

I hope this helps to clarify your understanding. Please let me know if you have any further questions.